Some features of oscillatory flow in a model bifurcation

Oscillatory flow in the lung is studied using an order-of-magnitude analysis and flow visualization experiments in a single bifurcation with lung-like geometry. The results are used to obtain a classification scheme that identifies three major flow regimes, distinguished on the basis of whether the flow is dominated by unsteadiness, viscous effects, or the effects of convective acceleration. The unsteady regime is found to exist for values of a dimensionless stroke length (L/a, i.e., stroke volume/local cross-sectional area) less than or equal to 3 and for values of a dimensionless frequency (alpha 2 = alpha 2 omega/nu, where alpha is airway radius, omega the oscillatory frequency, and nu the kinematic viscosity) less than or equal to 10 in basic agreement with previous studies. The viscous regime is found when alpha 2(L/a)(a/R)1/2 less than 10 and alpha 2 less than 10 where R is the local radius of curvature in the bifurcation; the convective regime is found when alpha 2(L/a)(a/R)1/2 greater than 10 and L/a greater than 3. This same approach yields scaling laws for the magnitude of secondary flow velocities and shows that the ratio of secondary-to-axial velocity is small everywhere outside of the convective regime where it scales with (a/R)1/2. Comparison of these results to related simple flows shows that many of the features observed can be attributed to the effects of curvature, suggesting that the influence of the flow divider and of area change may be of lesser importance than previously thought.     

Rheology and dynamic light scattering of silk fibroin solution extracted from the middle division of Bombyx mori silkworm

Dynamic light scattering (DLS) and rheological measurements were performed on aqueous silk fibroin solutions extracted from the middle division of Bombyx mori silkworm over a wide range of polymer concentration C from 0.08 to 27.5 wt %. DLS results obtained in the dilute region of C less than 1 wt % are consistent with a model that an elementary unit is a large protein complex consisting of silk fibroin and P25 with a 6:1 molar ratio. Rheological measurements in the dilute C region reveal that those units (or clusters) with the hydrodynamic radius of about 100 nm form a network extending over the whole sample volume with small pseudoplateau modulus mainly by ionic bonding between COO(-) ions of the fibroin molecules and divalent metallic ions such as Ca(2+) or Mg(2+) ions present in the sample and also that, after a yield stress is reached, steady plastic flow is induced with viscosity much lower than the zero-shear viscosity estimated from creep and creep recovery measurements by 4-6 orders of magnitude. Angular frequency omega dependencies of the storage and the loss shear moduli, G'(omega) and G' '(omega), measured in the linear viscoelastic region, indicate that all solutions possess the pseudoplateau modulus in the low omega region and samples become highly viscoleastic for C greater, similar 4.2 wt %. Above C = 11.2 wt % another plateau appears at the high omega end accompanied by a distinct maximum of G' ' in the intermediate omega region. The relaxation motion with tau = 0.5 s corresponding to the maximum of G' ' is one of characteristic properties of the fibroin solutions in the high C region. Thermorheological behaviors of the solution with C = 27.5 wt % show that the network structure formed in the MM part of the silk gland is susceptible to temperature and a more stable homogeneous network is realized by raising the temperature up to T = 65 degrees C.     

Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube

The effect of pulsatile flow on peristaltic transport in a circular cylindrical tube is analysed. The flow of a Newtonian viscous incompressible fluid in a flexible circular cylindrical tube on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The initial flow in the tube is induced by an arbitrary periodic pressure gradient. A perturbation solution with amplitude ratio (wave amplitude/tube radius) as a parameter is obtained when the frequency of the travelling wave and that of the imposed pressure gradient are equal. The interaction effects of periodic wall induced flow and periodic pressure imposed flow are visualized through the presence of substantially different components of steady and higher harmonic oscillating flow in the first order flow solution. Numerical results show a strong variation of steady state velocity profiles with boundary wave number and Reynolds number and a strong phase shift behaviour of the flow in the radial direction.     

Influence of aspect ratios on the creep behaviour of articular cartilage in indentation

Indentation tests are commonly used to determine the mechanical behaviour of articular cartilage with varying properties, thickness, and geometry. This investigation evaluated the effect of changing geometric parameters on the properties determined from creep indentation tests. Finite element analyses simulated the indentation behaviour of two models, an excised cylindrical specimen of cartilage with either normal and repair qualities and an osteochondral defect represented as a cylindrical region of repair cartilage integrated with a surrounding layer of normal tissue. For each model, the ratios of indenter radius to cartilage height (a/h=0.5,1.5) and cartilage radius to indenter radius (r/a=2,5) were varied. The vertical displacement of the cartilage under the indenter obtained through finite element analysis was fitted to a numerical algorithm to determine the aggregate modulus, permeability, and Poisson's ratio. Indentation behaviours of cartilage specimens for either model with a/h=1.5 were not affected by r/a for values of 2 and 5. Aggregate modulus was not greatly affected by the geometric changes studied. Permeability was affected by changes in the ratio of specimen to indenter radii for a/h=0.5. These findings suggest that experimental configurations of excised cylindrical specimens, also representing osteochondral defects with no or unknown degree of integration, where the cartilage layer has a/h=0.5 should not have r/a values on the order of 2 for confidence in the mechanical properties determined. Indentation of osteochondral defects where the repair cartilage is fully integrated to the surrounding cartilage can be performed with confidence for all cases tested.     

Extensional flow of erythrocyte membrane from cell body to elastic tether. II. Experiment.

This is the second of two papers on an analytical and experimental study of the flow of erythrocyte membrane. In the experiments discussed here, preswollen human erythrocytes are sphered by aspirating a portion of the cell membrane into a small micropipette; and long, thin, membrane filaments or tethers are steadily withdrawn from the cell at a point diametrically opposite to the point of aspiration. The aspirated portion of the membrane furnishes a reservoir of material that replaces the membrane as it flows as a liquid from the nearly spherical cell body to the cylindrical tether. The application of the principle of conservation of mass permits the tether radius Rt to be measured with the light microscope as the tether is formed and extended at a constant rate. The tether behaves as an elastic solid such that the tether radius decreases as the force or axial tension acting on the tether is increased. For the range of values for Rt is these experiments (100 A less than or equal to Rt less than or equal to 200 A), the slope of the tether-force, tether-radius line is -1.32 dyn/cm. The surface viscosity of the membrane as it flows from cell body to tether is 3 x 10(-3) dyn.s/cm. This viscosity is essentially constant for characteristic rates of deformation between 10 and 200 s-1.     

Efficiency of light diffraction by cross-striated muscle fibers under stretch and during isometric contraction.

When light is diffracted by a single frog muscle fiber the intensities I kappa of the different orders kappa (kappa = 1,2,3) strongly depend on the angle between the axis of the incident beam and the fiber axis. Maximum intensity is not obtained with perpendicular incidence (omega = 0 degree) but at angles that can be calculated for each order number and sarcomere length using Bragg's formula. In analogy to techniques developed for x-ray structure analysis of mosaic crystals we have rotated the fiber around an axis perpendicular to the fiber axis and to the incident beam axis within an angular range delta omega = +/- 35 degrees and recorded the light intensities I kappa. Diffraction efficiencies defined as E kappa = integral of I kappa d omega were studied as a function of sarcomere length and during isometric contraction. The sarcomere length dependences of the efficiencies E kappa of the first three orders show characteristic trends. E1 increases with fiber stretch, E2 has a minimum at a sarcomere length near 2.8 micrometers, and E3 has a maximum near 2.5 micrometers. These trends as well as the observed efficiency ratios are in fairly good agreement with predictions by the intensity formula developed for x-ray structure analysis. During isometric contraction, the diffraction efficiencies of the fiber decrease, with the decreases becoming greater the higher the order number. These decreases might be caused by a longitudinal displacement of myofibrils of up to 0.4 micrometers. The efficiency of light diffraction strongly depends on the tonicity of the bathing fluid. Hypertonic (3/2 x normal) solution reduces E1 to less than half, hypotonic (2/3 x normal) solution increases E1 to almost twice the value obtained in normal Ringer's solution.     

A laboratory study of the copper and nickel uptake and regulation in a copper-tolerant decapod, Cambarus bartoni (Fabricius) (Decapoda, Crustacea)

Tissue copper concentration in whole Cambarus bartoni, exposed for four weeks to 0.125, 0.25 and 0.5 mg Cu/litre and 0.2, 0.4 and 0.8 mg Ni/litre in the laboratory at 18 degrees C, showed a linear relationship with exposure time at 0.25 and 0.5 mg Cu/litre; the regression slope at 0.5 mg Cu/litre (r2 = 0.218; 0.001 less than P less than or equal to 0.05) was approximately two times higher than that at 0.25 mg Cu/litre (r2 = 0.148; 0.025 less than P less than or equal to 0.05). Regression analysis of nickel concentrations in whole crayfish as a function of exposure time showed a third degree polynomial relationship at 0.4 (y = 49.989 + 14.77x - 15.395x2 + 3.194x3) and 0.8 (y = 52.053 + 37.05x - 28.933x2 + 5.133x3) mg Ni/litre, as well as in the control (y = 49.126 + 27.253x - 23.468x2 + 4.168x3) (y = Ni concentration; x = exposure time in weeks), suggesting the occurrence of a Ni flux every 4 weeks.     

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.     

Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).     

Anion permeation in the proximal tubule of Necturus kidney: the shunt pathway.

The effect of foreign anions on transepithelial potential difference and transepithelial input conductance was studied in the isolated perfused Necturus kidney. Two microelectrodes (recording and current-injecting) were inserted into the lumen of single proximal tubules and the peritubular perfusate was shifted reversibly for 30-60 sec from a physiologic Ringer's solution to a test solution in which chloride was replaced isosmotically by a foreign anion. The permeability sequence, obtained by potential measurements, was: lactate less than glutamate less than gluconate less than pyruvate less than benzene sulfonate less than or equal to acetate less than or equal to F less than propionate less than BrO3 less than formate less than ClO3 less than Cl than ClO4 less than I less than or equal to Br less than NO3 less than SCN. Transepithelial conductance decreased when the tissue was perfused with anions less permeable than chloride but the conductance sequence was different from the permeability sequence. Such discrepancies were more pronounced during perfusion with hyperpolarizing anions; ClO4 and I- (both more permeable than chloride) produced an important decrease in transepithelial conductance, followed by incomplete reversibility when the perfusion was shifted again to chloride Ringer's. The results are best explained by the presence of weak positive fixed charges, governing anion permeation, at the shunt pathway of the proximal tubule. An analysis of the data allows tentative estimates of shape and size of the sites.     

A reexamination of the thermoelastic effect in active striated muscle

Isolated Rana pipiens sartorius muscles at 0degreeC were stimulated via their nerves and small stretches or releases applied during the plateau of the isometric tetanus at lo. Extra heat above the isometric maintenance heat was produced during the drop in tension caused by release and, for very small releases (delta less than or equal to 0.5% lo), was completely reabsorbed during tension recovery. The extra heat was always directly proportional to the tension change. Heat absorption proportional to the tension change was also observed during the increase in tension produced by small stretches in the range 0.5% lo less than or equal to deltal less than or equal to 3.0% lo. The mean heat:tension ratio R in seven experiments was -0.0084, which is within the range of values reported previously by Woledge. In addition, it was found that during tension recovery after small releases of 1.0% lo less than or equal to deltal less than or equal to 3.0% lo the "contractile" component seems able to shorten about 1% lo without producing shortening heat.     

The influence of link protein stabilization on the viscometric properties of proteoglycan aggregate solutions

The dynamic, steady-shear and transient shear flow properties of precisely prepared link-stable (s0 136, 66% aggregate) and link-free (s0 93, 59% aggregate) proteoglycan aggregate solutions at concentrations ranging from 10 to 50 mg/ml were determined using a cone-on-plate viscometer in a mechanical spectrometer. All proteoglycan solutions tested possessed: (1) linear viscoelastic properties - as measured by the dynamic complex modulus under small amplitude steady oscillatory conditions (1 less than or equal to omega less than or equal to 100 rad/s) - and (2) nonlinear shear-rate dependent apparent viscosities and primary normal stress difference under steady shearing conditions (0.25 less than or equal to gamma less than or equal to 250 s-1). Our transient flow data show that all proteoglycan aggregate solutions exhibited transient stress overshoot effects in shear stress and normal stress. From these steady and transient flow data, we conclude that link protein stabilized aggregates have significant effects on their dynamic and steady-shear properties as well as transient flow properties. The transient stress overshoot data provide a measure of the energy per unit volume of fluid required to overcome the proteoglycan networks in solution from a resting state. Thus we found that link-stable aggregates form much stronger networks than link-free aggregates. This is corroborated by the fact that link-stable aggregates form more elastic (lower than delta) and stiffer (higher [G*]) networks than link-free aggregates. The complete spectrum of viscometric flow data is entirely compatible with the proposed role of link protein in adding structural stability to the proteoglycan-hyaluronate bond. In cartilage, the enhanced strength of the networks formed by link-stable aggregates may play an important role in determining the material properties of the tissue and thereby contribute to the functional capacity of cartilage in diarthrodial joints.     

半夏凝集素在脂双层形成的阳离子通道

半夏凝集素是从多年生植物三叶半夏的块茎鲜汁中分离纯化的糖结合蛋白,具凝集素活性,与甘露聚糖有专一结合。本工作利用双室系统观察了它对人工脂双层的作用。 人工脂双层由卵磷脂和胆固醇(重量比为4:1)的正癸烷溶液形成。电阻≥10GΩ。在电压箝位下将半夏凝集素(1—4μg/ml)加至系统的一小室,几分钟后即观察到通道样活动噪音,脂双层电阻下降。甘露聚糖对这种变化有明显的对抗作用,加入40μg/ml的甘露聚糖可使脂双层的膜电阻立即从2GΩ恢复到对照水平(≥10GΩ)。在低浓度半夏凝集素和低维持电压下可获得单位电导涨落记录。在100mmol/L对称KCl溶液中记录的半夏凝集素单通道电流的优势电导为35pS。通过测定在非对称盐溶液中的平衡电位,根据Goldman—Hodgkin—Katz电位方程可推算出通道的离子选择性。结果表明,半夏凝集素形成的通道为阳离子通道。     

Electrodiffusion of ions approaching the mouth of a conducting membrane channel.

The movement of ions in the aqueous medium as they approach the mouth (radius a) of a conducting membrane channel is analyzed. Starting with the Nernst-Planck and Poisson equations, we derive a nonlinear integrodifferential equation for the electric potential, phi(r), a less than or equal to r less than infinity. The formulation allows deviations from charge neutrality and dependence of phi(r) on ion flux. A numerical solution is obtained by converting the equation to an integral equation that is solved by an iterative method for an assumed mouth potential, combined with a shooting method to adjust the mouth potential until the numerical solution agrees with an asymptotic expansion of the potential at r-a much greater than lambda (lambda = Debye length). Approximate analytic solutions are obtained by assuming charge neutrality (Läuger, 1976) and by linearizing. The linear approximation agrees with the exact solution under most physiological conditions, but the charge-neutrality solution is only valid for r much greater than lambda and thus cannot be used unless a much greater than lambda. Families of curves of ion flux vs. potential drop across the electrolyte, phi(infinity)-phi (a), and of permeant ion density at the channel mouth, n1(a), vs. flux are obtained for different values of a/lambda and S = a d phi/dr(a). If a much greater than lambda and S = O, the maximum flux (which is approached when n1(a)----0) is reduced by 50% compared to the value predicted by the charge-neutrality solution. Access resistance is shown to be a factor a/[2 (a + lambda)] times the published formula (Hille, 1968), which was derived without including deviations from charge neutrality and ion density gradients and hence does not apply when there is no counter-ion current. The results are applied to an idealized diffusion-limited channel with symmetric electrolytes. For S = O, the current/voltage curves saturate at a value dependent on a/lambda; for S greater than O, they increase linearly for large voltage.     

Effects of blood storage on rheology and damage in low-stress shear flow

Data are presented on the rheological and hemolytic behavior of whole human blood as it ages while stored at 4 degrees C (as in blood banking practice) up to 26 days. The viscometric properties of steady shear viscosity eta and oscillatory (complex) viscosity eta * = eta' - i eta" reported over ranges of shear rate gamma and radian frequency omega of 33 less than gamma less than 4130 s-1 and 1.5 less than omega less than 48 s -1; data on autologous plasma are given for reference. The Cox-Merz relation, eta (gamma) = [eta *(omega)] omega = gamma, is found to be a good approximation, with eta greater than or equal to [eta *], over the range studied. Release of hemoglobin (Hgb) and lactate dehydrogenase (LDH) into the plasma during shearing is tracked as a function of time for 30 min, and its sensitivity to gamma magnitude is measured. Bloods from four different donors are studied, with primary attention given to one (SSR). For all bloods, the release of both Hgb and LDH increases with storage age, but differences in such aging characteristics between different bloods can be substantial (even when rheological properties are identical). A post-shear incubation at 4 degrees C for one day shows no enhancement of plasma Hgb and LDH levels beyond those expected from normal aging after the shearing experience, demonstrating the absence of significant delayed-action effects as a consequence of shearing trauma.     

Exclusion of spheres by agarose gels during agarose gel electrophoresis: dependence on the sphere's radius and the gel's concentration

Agarose gel electrophoresis of spheres (radius = R) has been used to determine the effective radius (PE) of the pores of an agarose gel (percentage of agarose in a gel = A). The value of PE at a given A was taken to be the R of the largest sphere that enters the gel. When log PE is plotted as a function of log A, the results can be represented by: PE = 118A-0.74 for 0.2 less than or equal to A less than or equal to 4.0 (PE in nm). However, the data suggest significant nonlinearity in this plot, the magnitude of the exponent of the PE vs A relationship increasing by about 20% as A increases from 0.2 to 4.0. From these data, PE's as big as 1500 nm and as small as 36 nm can be achieved with agarose gels formed with unmodified, unadulterated agarose and usable for electrophoresis.     

The problem of determining the affinity of bivalent antibodies using ELISA and its mathematical solution]

A new approach for the determination of the affinity of monovalent receptors in direct coordinates could be obtained without using Klotz or Scatchard equations. The mathematical solution of the problem of the determination of the affinity of bivalent antibodies by ELISA gives the following relation between absorbance, measured in ELISA. and antigen concentration: omega + square root of omega 2 + omega = liK, where omega = (Ao-Ai)/Ai, Ai is the absorbance, if Ag concentration is equal li; Ao is the absorbance, if Ag concentration is equal zero, K is an equilibrium constant.     

Epithelial impedance analysis in experimentally induced colon cancer.

Epithelial impedance analysis was used to measure the alterations in resistance of the large bowel in a murine model of large bowel cancer. The technique was able to resolve the epithelial resistance from the total resistance of the bowel wall. A progressive decrease in resistance of the bowel epithelium occurs during carcinogenesis induced with dimethyhydrazine. About a 21% decrease in epithelial resistance from 22.0 +/- 1.3 omega.cm-2 to 17.5 +/- 1.1 omega cm-2 (p less than 0.025) was observed after 20 wk of carcinogen administration. The sensitivity of the technique in detecting altered epithelial resistance in premalignant bowel mucosa was improved by examining the impedance profile in a sodium-free Ringer's solution where the epithelium of control colons had a resistance of 24.4 +/- 1.8 omega.cm-2 compared with 19.0 +/- 1.1 omega.cm-2 (p less than 0.02) in colons from animals treated for only 4 wk with the carcinogen. Epithelial impedance analysis would seem to be a sensitive technique capable of identifying changes in the electrical properties or the large bowel early in disease states.     

Cryomicroscopic determination of the membrane osmotic properties of human monocytes at subfreezing temperatures

Monocytes were isolated from fresh whole human blood and resuspended in Hanks balanced salt solution; a portion of the cells was mixed with an equal volume of 2M dimethyl sulfoxide (DMSO) to form a 1 M solution. Microliter volumes of cell suspension were placed directly onto a computer-controlled cryostage and cooled to a predetermined subzero temperature. Ice was nucleated in the extracellular medium and a continuous video record was made of the subsequent osmotically induced volume changes of individual cells owing to exposure to the concentrated extracellular solutes. Selected micrographs emphasizing the initial transient data were digitized for computer analysis with an interactive boundary tracing algorithm to determine metric parameters of specific cells, and apparent volume changes were measured as a function of elapsed time after nucleation. The Kedem-Katchalsky-coupled transport equations were fit to the data using a network thermodynamic model implemented on a microcomputer to determine values for the permeability properties Lp, omega, and sigma. Experiments were performed over the temperature range from -7 degrees to -10 degrees C. Cells pre-equilibrated with DMSO had a lower Lp and a higher activation energy, delta E, than without additive, although the statistical significance of the difference could not be substantiated. It was found that the movement of DMSO across the plasma membrane in response to extracellular freezing was apparently so much smaller than the water flux that values for omega and sigma could not be determined from the data base.     

EPR study of the redox interactions in cytochrome c3 from Desulfovibrio vulgaris Miyazaki

We present a new examination of the EPR redox titration data for the tetraheme cytochrome c3 from Desulfovibrio vulgaris Miyazaki. Our analysis includes the contribution of the interaction potentials between the four redox sites and is based on the model previously developed for the study of cytochrome c3 from Desulfovibrio desulfuricans Norway. We observed, as for D. desulfuricans Norway cytochrome c3, that the conformation of the heme with the lowest redox potential, heme 4, is sensitive to the redox state of the heme with the highest potential, heme 1. However in D. vulgaris Miyazaki cytochrome c3 spectral simulations show that heme 4 is present in two conformational states which interconvert partially when heme 1 is reduced. The sets of redox parameters which satisfy the fitting procedure of the titration curves are in the following domain: -250 mV less than or equal to e41 less than or equal to -220 mV, -325 mV less than or equal to e2 less than or equal to -320 mV, -335 mV less than or equal to e3 less than or equal to -330 mV, -360 mV less than or equal to e4 less than or equal to -355 mV, -5 mV less than or equal to I12 less than or equal to 20 mV, -10 mV less than or equal to I13 less than or equal to 5 mV, -15 mV less than or equal to I23 less than or equal to -5 mV, -15 mV less than or equal to I24 less than or equal to -10 mV, -25 mV, less than or equal to I34 less than or equal to -15 mV. As in D. desulfuricans Norway cytochrome c3 the interactions are moderate. Simple electrostatic considerations suggest that these moderate values could be related to the large accessibility of the hemes to the solvent. Our work does not confirm the existence of a cooperative interaction between heme 2 and heme 3 which has been proposed on the basis of electrochemical measurements.